Dynamical behaviour of a predator-prey system encapsulating the fear affecting death rate of prey and intra-specific competition: Revisited in a fluctuating environment

Abstract

This paper revisits a population model incorporating a fear factor and intra-specific competition. An extension of the model from a deterministic framework to a stochastic one is also taken into account as an additional degree of realism. The prey-predator system in the absence of environmental noise is investigated in terms of equilibria, stability and positivity of the model. For this purpose, single parameter numerical continuation is performed to analyse the impact of fear factor in the reproduction and death rate of prey species, and the role of intra-specific competition in predator population. Then, the environmental noise is incorporated in the death rates of both species, leading to stochastic differential equations. It is demonstrated that the model has a global positive solution in the presence of white Gaussian noise and the extinction conditions of populations are analytically presented. Lastly, a deterministic approach to explore the statistical properties of the stochastic model is performed. The theoretical results of this paper are complemented with detailed numerical simulations.(c) 2022 Elsevier B.V. All rights reserved.